Modifications of the electronic bands of thin FeSe films due to oxygen vacancies in the supporting SrTiO 3 (001) substrate - and the interplay with spin-orbit coupling, magnetism, and epitaxy - are investigated by first-principles supercell calculations. Unfolded (k-projected) bands show that the oxygen vacancies both provide electron doping to the interface FeSe layer and also have notable effects on the details of the bands around the Fermi level, including renormalizing the width of the Fe-3d band near the Fermi level by a factor of about 0.6, and causing a splitting of ~40 meV at the M point for the checkerboard antiferromagnetic configuration. For an FeSe bilayer, the modifications to the bands are mainly limited to the interface FeSe layer. While spin-orbit-coupling induced band splittings of ~30 meV at M for the ideal FeSe/SrTiO3 (001) interfaces are comparable to the splitting due to oxygen vacancies, the effects are not simply additive. Calculations and comparison to our scanning tunneling microscopy images of MBE-grown FeSe films on SrTiO3 (001) suggest that a common defect may be Se bound to an oxygen vacancy at the interface
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